This disclosure relates to phase-shifting interferometry.
Interferometric optical techniques are widely used to measure optical thickness, flatness, and other geometric and refractive index properties of precision optical components such as glass substrates used in lithographic photomasks.
For example, to measure the surface profile of a measurement surface, one can use an interferometer to combine a measurement wavefront reflected from the measurement surface with a reference wavefront reflected from a reference surface to form an optical interference pattern. Spatial variations in the intensity profile of the optical interference pattern correspond to phase differences between the combined measurement and reference wavefronts caused by variations in the profile of the measurement surface relative to the reference surface. Phase-shifting interferometry (PSI) can be used to accurately determine the phase differences and the corresponding profile of the measurement surface.
With PSI, the optical interference pattern is recorded for each of multiple phase-shifts between the reference and measurement wavefronts to produce a series of optical interference patterns that span a full cycle of optical interference (e.g., from constructive, to destructive, and back to constructive interference). The optical interference patterns define a series of intensity values for each spatial location of the pattern, wherein each series of intensity values has a sinusoidal dependence on the phase-shifts with a phase-offset equal to the phase difference between the combined measurement and reference wavefronts for that spatial location. Using numerical techniques known in the art, the phase-offset for each spatial location is extracted from the sinusoidal dependence of the intensity values to provide a profile of the measurement surface relative the reference surface. Such numerical techniques are generally referred to as phase-shifting algorithms.
The phase-shifts in PSI can, for example, be produced by changing the optical path length from the measurement surface to the interferometer relative to the optical path length from the reference surface to the interferometer. For example, the reference surface can be moved relative to the measurement surface or a modulator may be placed in one of the beam paths. Alternatively, the phase-shifts can be introduced for a constant, non-zero optical path difference by changing the wavelength of the measurement and reference wavefronts. The latter application is known as wavelength tuning PSI and is described, e.g., in U.S. Pat. No. 4,594,003 to G. E. Sommargren.
The interference signal in a PSI system is typically detected by a camera system, converted to electronic data, and read out to a computer for analysis. In conventional applications, the optical interference signal is imaged onto an array of pixels. Charge accumulates at each pixel at a rate that depends on the intensity of the incident light. The charge value at each pixel is then read out, or transferred to a data processing unit.
The rate at which a camera can detect and read out an image is known as the frame rate. The accumulation and read out process can be slow, particularly for detectors with a large number of pixels. Conventional camera frame rates are typically limited to a few hundred Hertz for large-format (e.g., 1 Mega Pixel) cameras.
Such conventional PSI systems are, consequently, limited to phase shift rates less than the camera frame rate. When the phase of a PSI system is shifted faster than the frame rate, the camera system will integrate together interference patters with multiple phase values, making the measurement of an interference pattern at a distinct phase values impossible. Unfortunately, a PSI system operating at a relatively low phase shift rate is highly susceptible to noise. The fact that the measurement requires time means that other time-dependent phenomena, such as mechanical vibrations, tend to be convolved into the data, resulting in measurement errors.